Solve ∫ xcosx wrt y

$$\int x \cos x d y$$

Evaluate

$$xy\cos(x)+С$$

Solution Steps

Find the integral of x\cos(x) using the table of common integrals rule \int a\mathrm{d}y=ay.

$$x\cos(x)y$$

If F\left(y\right) is an antiderivative of f\left(y\right), then the set of all antiderivatives of f\left(y\right) is given by F\left(y\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$x\cos(x)y+С$$

Differentiate w.r.t. x

$$y\left(-x\sin(x)+\cos(x)\right)$$